Travel our First Day

I just figured out what our cumulative flight distance will be on our first day: Roughly 10,000 miles. Since the circumference of the Earth is 24,901 miles, I guess you could say we're traveling almost half-way around the world for this trip! (Lots of frequent flier miles!!) The trip is a full 24 hours from wheels up to landing. The strange part will be the last leg, from Amsterdam to Cape Town, which is roungly 11 hours, with no change in time zone, but a change in season, from Fall to Spring. I guess that last leg will give us time to recover from jet-lag. Will we need time to recover from season-lag??